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RobustH∞control based on fuzzy hyperbolic model with time-delay

Authors
Journal
Progress in Natural Science Materials International
1002-0071
Publisher
Elsevier
Publication Date
Volume
18
Issue
11
Identifiers
DOI: 10.1016/j.pnsc.2008.05.014
Keywords
  • Robusth∞Control
  • Fuzzy Hyperbolic Model (Fhm)
  • Delay
  • Linear Matrix Inequality
Disciplines
  • Design

Abstract

Abstract This paper investigates the problems of robust stabilization and robust H ∞ control for the fuzzy hyperbolic model (FHM) with time-varying delay. A kind of novel Lyapunov–Krasovskii functional is constructed. By using the descriptor model transformation and free-weighting matrix technique, new delay-dependent sufficient conditions for the existence of desired FHM controllers are developed in terms of linear matrix inequality (LMI). The designed controllers not only ensure that the closed-loop system is asymptotically stable, but also satisfy a prescribed H ∞ performance level. The matrices of the Lyapunov–Krasovskii functional are not required to be diagonally positive-definite. In addition, the traditional restriction that the derivative of the time-varying delay is strictly smaller than one is not needed. Therefore, the obtained results are less conservative. Finally, a simulation example is provided to show the effectiveness of the proposed methods.

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